{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qanneal.sdeq import IsingHamiltonian, ket2dm\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 5\n",
    "h = {}\n",
    "J = {(0, 1): -1, (0, 3): 1, (0, 4): -1, (1, 2): 1, (1, 4): -1, (2, 3): -1, (2, 4): -1, (3, 4): -1}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "ising = IsingHamiltonian(h, J)\n",
    "ising.induce_transverse_field()\n",
    "# ising.induce_highord_driver(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "annealing_time = 1000\n",
    "num_steps = 100\n",
    "tlist = np.linspace(0, annealing_time, num_steps)\n",
    "spectrums = ising.energy_spectrum(tlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(spectrums.time / annealing_time, spectrums.energy)\n",
    "plt.xlabel('s')\n",
    "plt.ylabel('energy')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "expects = ising.solve_sdeq(tlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dGTBgAAMGDGDevHn39L5CCO0l7/+Rb786i1nnR8vG6Tz2xBitSxIurlSH7L777jvWrVvH7NmzKSgoYMSIEQwYMAA/vztfayolJYV58+axatUqPD09GTFiBB07diQ8PPym58ycOZNdu3bRsWPH4sePHDnCSy+9RGxsbBk+mhBCK0e2bOTH7RZUxZN2bQp4qM/jWpck3ECpRkje3t4MGTKEFStWMGPGDD788EMeeeQRXnnlFTIyMm67zc6dO4mKiiIwMBBfX19iYmJITEy86TkJCQl0796dPn363PT4kSNHiI+PJy4ujj//+c9kZ2ff58cTQpS3PevWsmu7HYDoLh481Ke/xhUJd1HqSQ1bt27lq6++Yt++ffTv35/BgwezZcsWJk+ezIoVK255fmpqKkajsXjZZDJx+PDhm54zYYJjps2+fftuetxoNPLMM88QGRnJ3LlzefXVV5kzZ06pP1RISNmvEmw0+pf5Ndyd9MBB+uBQmj4kfPAhh34OwkMtIHZ4GM2jO5VDZeVH9gUHZ/WhVIH06KOPEhQUxKhRo3jrrbfw9vYGICIiguXLl992G1VVb3lMUZRSFbVgwYLi/54wYQI9evQo1Xa/ysjIxW6/9f1Ly2j0Jy0t5763rwikBw7SB4fS9GHD4o84m1YPb/t1ej0egalRswrVO9kXHMrSB51OueuAoVSH7N566y1Wr17NsGHDisMoOTkZgE2bNt12m9DQUNLT04uXU1NTMZlMJb5XTk4OH3/8cfGyqqryS24hXNyadxdzJr0BVWypxI1vT83GzbQuSbihuwbS9evXuX79Oq+99hrZ2dnFy+np6UyZMuWuLxwdHc2uXbvIzMykoKCApKQkunTpUmJBvr6+LF68mEOHDgGwdOlSevbseQ8fSQhRXiwWM1/NXvLfG+tNjSG4Rm2tyxJu6q5Dj+eff54dO3YA3DQLzmAwlHgYLTQ0lGnTpjF27FgsFgtDhw4lMjKSiRMnMnXqVFq2bHnb7fR6Pe+88w6zZs2isLCQevXqMXv27Hv9XEIIJ8vNzmTte+vI1ocTrJxh0J9Hye0jRJko6u1O9vyPv/71r7zxxhvlUc8DIeeQyk564CB9cPjfPqSdP8N/PttHnsFETZ9T9Pv9uAp/aF32BQdnnkO66x50+vRpGjZsyJgxYzh69Ogt65s3b35fRQkh3NfpA7vZuu4qZn0I4aZz9HxarksnHoy7BtI//vEPFi1axB/+8Idb1imKcscJDUKIimn/hnXs36vHrvjQqmkWDw98UuuSRAVy10BatGgR4LhSgxCicvt+2TJOng/FoBbSuZs/zTr10rokUcHcNZD+/ve/33XjGTNmPNBihBCu6eNX3uVCdn187Zn0fLypTOsWTnHXQAoMDCynMoQQrqjIbCb+nWVkqA2par9E7KSeBFQr+feEQtyPuwbSs88+W151CCFcTHb6NRI+2ESOoSFG/Wnipo2Wad3Cqe4aSCNHjuSLL76gTZs2t73sz/79+51WmBBCO2cP72fL2vMU6GtSp2oyT818TqY8C6e7ayC9++67AHzzzTflUowQQnt71q3l0EFP7Do/mjdIoctwucOrKB93DaRfrz1Xq1Yttm3bxs6dOzEYDHTt2pV27dqVS4FCiPKzYcnHnE2ti6eaR/SjPjTrNELrkkQlUqqLq37wwQe88cYbeHt7o9frmT59+l3vACuEcC9FZjNfvbWEM2n18bWlETumKc06ddW6LFHJlOpaH9988w0rVqwovkPsU089xahRoxg9erRTixNCOF/m1QusX7KdHEM4wZxh4J+G4eVb9nuKCXGvShVIXl5eVKlSpXg5ICAAL5ltI4Tb+/mH7ezcmIFZX4O6VZPpN0XOFwnt3DWQkpKSAKhfvz5Tpkxh2LBh6PV64uPjadGiRbkUKIRwjq3Lv+TE6RAUxZvIiAyiB0sYCW3dNZA+++yzm5Y/+uij4v/OyMhwTkVCCKeyWq18s+BjruaH42PP4pF+tWjYJkbrsoS4t0ASQri369eusH7JJrL1jQiwX6DfpBi58oJwGaU6h3Tu3DmWLl1Kfn4+qqpit9s5f/48X375pbPrE0I8IMd3beGHTdcp1Nemhs8pYivBPYyEeynVtO/nn38ei8XCgQMHqFWrFsnJyTRu3NjZtQkhHpBNn3zGtu8tWBUvWjVOZ+AfJ0gYCZdTqkDKy8vjlVdeoXPnznTp0oWPPvrotjfsE0K4FnNBPl/NXsLJq3Xxsl+n54BQoocM07osIW6rVH8i/XrV77CwME6dOkVkZCR2u92ZdQkhyujKyWNsXPETeYZwgjlN3HND8fGrqnVZQtxRqQIpLCyM119/nUGDBjF9+nTy8/MpKipydm1CiPv049pVHDnig00XQoNqZ4iZ8LTWJQlRolIF0qxZs9i6dSvNmjXj8ccfZ/v27bz66qvOrk0IcY8sFjPfvPcZKYUN8VRz6RCtJ7LbU1qXJUSplCqQfHx86NChA99//z21a9fmjTfeoGpVGfoL4UpSzp7i22V7yTE4pnT3Ht+N4Bq1tS5LiFIrVSBt3ryZF198kfDwcFRV5cKFC8ybN4/27ds7uz4hRCn8sGYVR3/yxqIPpW7VZGKeeVJm0Qm3U6o99t1332Xp0qU0atQIgKNHj/K3v/2NVatWObU4IcTdFZnNfLPgM1LMDfFSc4nqUETr7nIJIOGeShVIiqIUhxFA8+bNUVXVaUUJIUp28fhhNq88Tq6hEYHqefpM6EFg9ZpalyXEfbtrIF2/fh2AFi1asGTJEkaMGIFOp2PVqlVERUWVR31CiNvY/PnnnDobgl0XQr2g0/QcP1YO0Qm3d9c9OCoqCkVRikdDb731VvE6RVF48cUXnVudEOImudmZrP8gngy1IT5qJh0fC6bpwzKlW1QMdw2kEydOlFcdQogS/LRlE3u35VBgaEiIcpq+fxiIX0Cw1mUJ8cCUaoxvt9tZsmQJW7duxWq10qlTJyZNmiSHCIQoBxaLmf988BlXcupjULxpFnaFriNlVCQqnlIlypw5czhx4gRPPvkkdrud5cuX849//IPp06c7uz4hKrULxw6xZZVj4oK/epnuw9tSI7y31mUJ4RSlCqRt27axcuVKPDw8AHj00UeJi4tzamFCVHYbP/mUs5eqY9dVo07VZHrLb4tEBVeqvVtV1eIwAvD09LxpWQjx4KRfOkvSp9vI1oXhq6YT1T2UiCj5bZGo+EoVSE2aNOH//u//GDNmDADLli2T+yEJ4QRbl3/JyeQArLo6mDxOETt1BF6+flqXJUS5KNX9kGbOnMmNGzcYMWIEw4cPJzMzk7/97W8lbpeQkEDfvn3p2bMny5Ytu+PzXnzxxZuu+nDlyhVGjx5N7969mTx5Mnl5eaUpUwi3lXn1El+++TFHz9ZAr5rp2K6AIc9PkDASlUqpRkj/+te/ePPNN+/phVNSUpg3bx6rVq3C09OTESNG0LFjR8LDw296zsyZM9m1axcdO3YsfvyVV15h1KhR9OvXjwULFvD+++/zwgsv3NP7C+Eudny1ghM/V6FIH0Y1QzJ9Jg+S6dyiUirVCGnz5s33/MI7d+4kKiqKwMBAfH19iYmJITEx8abnJCQk0L17d/r06VP8mMViYc+ePcTExAAwePDgW7YToiK4fu0Ky9/8iMOnQ9Fho32rHIa9MF7CSFRapRoh1a5dm6effpq2bdtSpUqV4sefeurO91lJTU3FaDQWL5tMJg4fPnzTcyZMmADAvn37ih/LysrCz8+veDaR0WgkJSWlNGUWCwkp+2EOo9G/zK/h7qQHDs7oQ8Kijzh61IcifX2MhtOMenkkASGmB/4+D5LsD9KDXzmrD/d0C/OjR4+i1+vx9y+5mNtdfFVRFKdt91sZGbnY7fd/8Vej0Z+0tJz73r4ikB44POg+pF86y7efbeW6Ug9vrtMu8gbt+z1NkR3N+m2z27AU2bBaLRRZrOh1Cl5e3nh6GtDpHAdRZH+QHvyqLH3Q6ZS7DhhKFUgTJkzgL3/5C8ePH0dVVR566CFmz559121CQ0PZu3dv8XJqaiomU8l/AQYHB5Obm4vNZkOv15OWllaq7YRwZVarlc2ffc65KyasurqYDMnEOPlckd1uJy09g4sXLpKacpW8G5kU5edgNeehWvLR2QvRqUUYVAu3+5tPVcGmGLDhgar3QtV5offyx8svEL+qIZiq16BheEOCAgOc9hlE5VKqQHr55Zd5/PHHGTx4MKqqsnz5cqZPn85HH310x22io6OZP38+mZmZ+Pj4kJSUxGuvvVbie3l4eNCuXTvWr19P//79iY+Pp0uXLqX/REK4mHNH9rN97Qly9GH4qBm068ADv2fRjZxcfj5xkisXz5KTmYI1Px0P63UMWIufY1cV7IoX6H1QDL4oHkHoPX3Qe/mgN3ig1xvQ6fSoqh2r1YLNagFLEWpRIdjNWM35qHlXseWcJueaSs5JOL0VzPii+lSjqrEudes3oknTJlTx9Xmgn09UDqUKpIKCAoYPH168/MQTT7BixYq7bhMaGsq0adMYO3YsFouFoUOHEhkZycSJE5k6dSotW7a847YzZ87kpZdeYuHChdSoUYO5c+eW8uMI4TqKzGYSF33GtZx6qIqJWr7JxEwciZePb5le1263c/7CJU6eOEba5TPYcq7gZbtRPMpR8UbxDEIJbkqV4FCMoTWoWasWNauHojfo7+s9f3uYxma1kZKaxoXz57l25QJFGVdR81IounCB5AvbOblZocgrlIAajWjSojWNGzUsPvQnxN0oainutPf73/+e8ePH07ZtWwBOnjzJvHnzWLhwodMLvB9yDqnspAcO99uHg5sSObQrj3xDNfytV3i4X0Matulw33VcuHiZYz8dJu3iKci9hCeFAFjwxOYdil+12tSq04DGTSIIDgq87/e5k9L0ISMji+PHj3P53CkK00/jbb8OgFnxw6d6c9p2jKZhg/oPvLbyIv8mHJx5DqlUgTR06FCOHz9OREQEBoOBY8eOYTQa8fNzvHBCQsJ9FecsEkhlJz1wuNc+ZF69xMZPk8i018dgNxNWM5VuT4y652vQFRYWcfDgQc6d/Alzxmm8VUcNRXiDX21CajakUZOmNGgQhl53f6Oee3E/+8PVa6kc2r+PlDOH8DJfQVGgQB9C9UYdeKRrV6pUKdtIsbzJvwkHzSc1/OUvf7mvNxeisrBarXz36VIuXA3FomtAsHKW7k8+SrXapb8yd0ZGFvv27uba2WPo8y9iwIpd1YFPTXxrtadp81Y0aBDmNoe/alQ3UaNvH6APKalp/LhjG4XnD5B94j/En/gWXXBTorrFUD+srtalChdRqhGSu5ERUtlJDxxK04eftmxi/7Z08gzV8bWm07K9N21j+pXq9dPSM9jzwy7Szh3B03wNnaJShA/6oPqENY6kdZs2LjFB4EHtD3a7nYOHjnB07xYMN86gYKeoSn1ad4ohsmWzB1Cp88i/CQfNR0hCiFtlXr3Exs+SyLTVR68EUadqMr3Gj8HTy+vu22Vls3vXTlLOHMTLfNUxGUHxR1+jHU0jH6JZs4hyOQynBZ1OR9s2rWjbphUpqWls+fY/6FMOcfzbDziwtRbtusXRvFlTrcsUGpFAEuIeWSxmNn38OZdSq2PRNSBIOUe3UZ0Ird/rjtvk5eXzw65dXDq5H8+CS+gU1RFCNTsQ2TaKRo0auM2huAcl1GTk8dFjycnJZVNSIpbzP/BT4kL2ba1Pp16DaNigntYlinImgSTEPdiftI4juwvINzTAV02nbRsbbXuPu+1zbXYb+/ce4MShXehvnEGv2FDwQRfahpZto2jSpHGlC6Hb8ff3Y+CQodzI6U3SujXor+xj9+p57DW1oe/Aofj7yxXPKwsJJCFK4cKxQ+yIP8h1JQwPRU/9kDN0HzcKD49bD89dvHiZ3Tu3knflMF5qHjo8UIMiCG/VkdZtIivs4biyqurvx9ARo0lL703SmuXo0vYT/+9j1GwZQ7fu3SS8KwGZ1HAbcvJSevArvS2XFe98Sbq5PqqiEGI4S/cxMQTXqH3T83Jz89ixfRvXTu3D2+K4GHChZ01qN2lPdKdofHy0n5hQFlrsD4eO/MSB777Gx5ZJoXdteg4cS82a1cu1ht+SfxMOMqlBiHJWZDaz8aNlXMmogUXfiAD1Ah16Nya87X8v+WO32/np6AmO7NkC1085LtOj+OFRO5r20V2oU7umhp/A/bVq2YIWTZuyfl0CtuQtfP/lbIIadyemb28ZZVZQEkhC/IbVamXHV19x5rQPhYaGVFHTiGxRRIfYJ4qfcyMnl22bvyf99F687Vkoqh57QDiN23WmVWRLObT0AOkNevoPGMiFi+35fs2n5JzcwNLzP9F72NOEmowlv4BwK3LI7jZkaF45e7A/aR1Hd+eSa6iOl/UGYXWuM/S5Z8jKKsBut3P02M8c3r0FJetn9IqNQn0Qxobt6fRIVwICKvZ9clxhf7Db7SSuX8/1nzdhV/SEtR/II490Lrf3d4UeuAI5ZCeEE53cvZO9354mW18Xg6Kntl8yPcYNw8evKrl5+axL+Ib0M3vxtv06GmpEi46P0qJ5ExkNlSOdTkff2FiSmzRnx7qPubJnBZ8nH2PwyCfx9r77b7+Ee5AR0m3IX0KVowcXjx9m55p9ZKn1UFQb1TzP0W10b4Jr1ObIT8c5vHszyvWT6HGMhqo1aEfnLl0JCKiqdenlztX2h8LCIuK/WoqSdpACfTCPDZ5I3Tq1nPqertYDrWh+cVV3I4FUdhW5B1fPnGD71zvItNZDVRSCdOfpNLA9QXUasm3LZq6d/BEfWyY2VY8uJILm7brQvFnlHg256v6wbet2LuxdjQrUaz+Yzo90ctp7uWoPypscshPiAUi/dJYtX24io6geNqUBgVygfUwTdEGPsX3bJqzrPsIDC4ougCrhPXikazfCw2vKl5ALe6RLZ87Xq8fm1f/m8p7lrLx6gUFDh1fqPx7cmQSSqPAyLp1n8/JvyTCHYdM5pnBHPlKTTLUBO3Z+j3fRFVRVQfVvQKN2XWndOlK+0NxIWN3aDP/dX/nqs8VwaRdL/53CkCd+5xIXpRX3RgJJVFhp58+w9evvioOoqnqR+i2qcDVPz4E9SXhSgIIPHnU60bnrY5hkGrHb8vb2ZvT4KaxdvQr13Fa+/vc/6Pn4JGrW0O6HtOLeSSCJCudq8gl2rN5BpuXXILpASF0LqTeuc/7n8+gUFbtXLWq0jObh6Cg8DB5alyweAJ1Ox8AhQ9mxoybnfvyaTV/Mo32/CTSJaKR1aaKUJJBEhXHuyH52rz9Ili0Mu9KQAPUMXiE3yMtNJftaLjo80YW2IeqR7oSF1dG6XOEknTpFE1LNyJ51i9m3biHZ2SPp2KG91mWJUpBAEm7v511b2b/5DNnUBepRVTkGflkoRRlYc+yoHiaqNe1Op86P4O3tqXW5ohw0iWhE1arT+Hb5+5zZtpTsrCx6xdz59iDCNUggCbe1Z91aTh7M4YauFno1lADDbmyGLPQUYLV4oFRrQdtOj9EovIHWpQoN1KxRnYFPvUD8Z++RdfQb1hbkETdwkNZlibuQQBJupchsZvtXX3HpnBd5BiNeujyCDJtQdTcct/82VMPYuBudu3SVWVaCgAB/hk94nhUfL4Az3/PVF3kMGT5KZlG6KAkk4Ray06+xbfk6UrNMFBlM+BpOEuTxI4pShBUDSnBzIqMepWmTxlqXKlyMt7cnoydM5ctP/oXh6m6+/DSf4WPHyxXDXZAEknBpyft/5MDGo2RZa6Po/anieQBffTqKAgUGIzUjOtDpkS4yGhJ3pTfoGfnUJL76/DP0qfv44sOFjBw3Gb1BQsmVSCAJl2OxmPlhdTwXTlnJ1QXipS+kqmcSiq4IC57oqrWmzcNdadyoodalCjei0+kYNuoJVn/tCZd28fmH8xk+7vd4esq0f1chgSRcRsal8+xY/S0Z2SHYPYvw9jxLgC4dALN3TWo36UCnTtF4e3trXKlwVzqdjiGPj2TNKk84t4Uvl/yTx5/6g8y+dBESSEJzB75dz897U8jFF0/DDXx8jqIoNsz44lWzIx07d5O7r4oHasDgIaxL8IRT37L8w3cY/vRzEkouQAJJaOL6tSvsiP8P6RneqJ438PQ4j78uH7uqwxrQmKZtHqZ1m0g58Sycpl///qxfp4OfN0gouQgJJFFurFYrBzas5/ThNAp04KG/jLdPOqoKFk8jpogePNwpmipVfLUuVVQSffv1Yz1IKLkICSThdBePH2Zv4g/kFCooHpl4eF7FV7FjwwuPWg8T1aWbXARTaKZvv378BySUXIAEknCKnKwMdq1KIDWlALtHHh66q3h5WVBVPWpgOE3bPUrLls3kB4rCJfT5zUhpxUfzGTF+qsy+04AEknhgLBYzuxPWcuHnFCz6Ijz0V/HwNqOqOuzeRsLa9uCh9m3l6trCJfXt149vbDZI3siXH77HyAnPyr5aziSQRJlYrVYOf5/EqQPJFKkW9IZU9F4FeKoKqr4qppa9iYqOxsdHfrgqXF9sXBxr421w5nu+/PB9Rj39rPx4thw5NZASEhJYuHAhFouFcePGMXr06JvWHz9+nBkzZpCbm0u7du145ZVXMBgMxMfH8/bbbxMSEgLAo48+yrRp05xZqrhHhzd/y4k9xyiyF6EzpKM3FOChKqBUIbBRd6If7Y6/v5/WZQpxz+IGDiJ+pQ3Ob+WLjxcy8unJMtuznDgtkFJSUpg3bx6rVq3C09OTESNG0LFjR8LDw4uf88ILL/D3v/+d1q1b8/LLL7NixQpGjRrFkSNHeOmll4iNjXVWeeI+HNr8LT/vOUKRvQi9IQOd3oxBpwBV8A+LplOPfgQE+GtdphBlNnDIUFYut8DlXSz/ZDEjnpyodUmVgtMCaefOnURFRREYGAhATEwMiYmJPPvsswBcvnyZwsJCWrduDcDgwYP55z//WRxI58+fZ9GiRTRu3Ji//e1vBAQEOKtUcQdWq5X9367n7E8nsapF6PQZ6PQWDDod4EdAvYfo1DNWRkKiQho0bDhff2FBn7KXFUs/5vfT/qB1SRWe0wIpNTUVo9FYvGwymTh8+PAd1xuNRlJSUor/+5lnniEyMpK5c+fy6quvMmfOnFK/d0hI2b8gjcbK+Zd+fm4O6z9ZytVzl7EpZvS6TBS9Hb2qR8GPGk3b0nvosEp1MdPKui/8r8rYh8lTJ/Ov+e9hu3aAxR/8m2em/E7rklyCs/YFpwWSqqq3PKYoSqnWL1iwoPixCRMm0KNHj3t674yMXOz2W1+/tIxGf9LScu57e3dzOfk4ezZ8S0FuLqo+D70uB8UAersXihJIjebtierWq3gabH6elfy8ytGfyrYv3Ell7sPgEU/yxcdmuPgDixYaGDT0ca1L0lRZ9gWdTrnrgMFpgRQaGsrevXuLl1NTUzGZTDetT09PL15OS0vDZDKRk5PDypUrGTduHOAILoNBJgM+SFarlR/Xr+HSyWRsdjOKPhudYkExKGCvgt6jBu16D6BuwybyOyFR6el0OkaMncjyTxZSdGE7CWu86D9ggNZlVUhO+6aPjo5m/vz5ZGZm4uPjQ1JSEq+99lrx+lq1auHl5cW+fft46KGHiI+Pp0uXLvj6+rJ48WLatGlDq1atWLp0KT179nRWmZXGpZNH2btxIwU5Oaj6AvS6HNCBDk+w++FrrE503OOEBDtmNlbmv4iF+F96g55Jf3qe9978Pzi9iQ2JXsT07q11WRWOU0dI06ZNY+zYsVgsFoYOHUpkZCQTJ05k6tSptGzZkrfffpsZM2aQl5dHs2bNGDt2LHq9nnfeeYdZs2ZRWFhIvXr1mD17trPKrLByb2Sxc+1qsq5ew6aa0emzURT7L6MgPxRdKGGtO9C+S3cZBQlRCl6enjz+1B9YvmQeWUfX852nF4891k3rsioURb3dyRw3VxnPIVksZn78zzdcST6J1WpG0eeiU4oAsNt9UfDB31id6P7DCQoOLPH13LEHziB9cJA+/LcHefkFfL1kDp5FadTuMIxHHumsdWnlyi3PIQnnMpsL2LcxkcsnT2K1FIIuH52uAABF5wX2Knj4Vqdl1140ahGpcbVCVBxVfH0YNO45Vn00l0u7v+ZHTy86dmyvdVkVggSSm8i/kc2OdfFkXbmC1WZG0eehU8wAKHoPVHsVdLpAwiLb0u7RnnIYTggnqurvR9wTfyThkzmc3v45BoOBhx5qo3VZbk8CyUWdP3WcI1u+Iy8rC5tahE6fi6JYQQFF5w02X3SewdRq2oKHuvXCy9NL65KFqFSCgwLoO+aPrF86jxNbPsNg8KBVqxZal+XWJJBcgNlcwL5NiVw5dQqLuQB0hShKHooC6EGx+6LaquLp60f4Q1FEPly5jlkL4aqM1ULoNWIq337xDj9t+ggPj4k0a9ZE67LclgRSOSsqKuLoj9s5d+QQ5rxcVIoc538UCwCK3oBqr4KimvANCiKyaw/CGkVoXLUQ4k5qVDfRbdizfL/in+xPXIxeP4mIiPCSNxS3kEByoqKiIo7v2cHZw4cozM1BxfJL+Dhmv6Fz/BAVW1X0nt5UbxhOu1598PaSW3gL4U7q1K5J1yG/Z+vK99iz7l/o9JNpFN5A67LcjgTSA1KQl8/+LRtIOX2GosL8X0Y+Bb8JH0CtAjY/FIMXgaHVadOtF8aatTStWwjxYISF1aHToCnsWL2AH9Z+gG7gZBo2qK91WW5FAuk+nDy8j1P79jgmHFiLQClC0eWjKDbHE4pHPo7wCTCG0vrRHoTWqatt4UIIp2pQPwx14GR2xr/PzviFKIN+T4P6YVqX5TYkkO7i8vmzHN25hRspKViLzKiK5eZRD4DeA+y+YAtC7+VNcK3atOnWi6CQatoVLoTQTMMG9bH1n8TuhA/YsXoB6sApNGxQT+uy3IIE0m8UmvNZM38udtUMihmdrvC/K/X6X4LHH0VvwKdqAPVbtKbxQx3w9PTUrmghhMtp3Kghauzv2P3Nv9gZ/z5q3GTCw+XwXUkkkH5DpxiwqwWgqI7wwTHVumZ4I1p17SaTDYQQpRbROBxd3GR+WPsBu9a+j73/JBo3aqh1WS5NrmV3G3LdLunBr6QPDtKH++/B6TNnHeeTsNO290SaNXPvn3E481p2cn0ZIYRwooYN6tN58LPYMXAgcREHDh7SuiSXJYEkhBBOVr9eXboP/yNWxZvjmz7mxx/3aF2SS5JAEkKIclCrVg36jPkTFr0/Z7Yv4/vvN2tdksuRQBJCiHJiMoYQN+55zJ7VSNm/ioQ18VqX5FIkkIQQohwFBQYwfMLzFPmGkX/6O5Yv/QSb3aZ1WS5BAkkIIcqZj48Poyc+hy2oBaTu4/PF71FQUKB1WZqTQBJCCA3oDXpGPDkBz7qd8cw9zfJ/v0VqaprWZWlKAkkIITSi0+kYNPRxqj80DE9LFolL53D8+M9al6UZCSQhhNBY166P0LrPJEDlwPoP2Ji0UeuSNCGBJIQQLqBZswh6j/kzFs9qZPy0ls8/WkRhYVHJG1YgEkhCCOEiTCYjoyb/BUxt0Wf9xJeL3uT8+Ytal1VuJJCEEMKFeBg8GD5mHNXbDsXDms32lfPYkJiI3W7XujSnk0ASQggX1PXRLjw6/M9YPUK4fmw9Sxe9S0ZGltZlOZUEkhBCuKhatWowZvJLeIU9gkfeOf7zyeskbUiqsKMlCSQhhHBheoOegUOG0bb/H7AaAsg6+g2fvf8Pzp67oHVpD5wEkhBCuIGIxuE88ezL+DfuhaEojR9WzuGLT5eQmXVd69IeGLljrBBCuAm9Tk/f2FhSUzvy7Tcr0acd4j8fHaNKWBQ9Yvri51dF6xLLREZIQgjhZkwmI6OfnkTbuD9i9Q7FfH4b8Ytm8vWXy9x6xCQjJCGEcFONGzWkcaO/cOjQTxzcmYjtyo8kfrgXNSiCyA5daN6sCTqd+4w7JJCEEMLNtWrVglatWnDy1Gl2b9mALutnjiUdY//GQALrtqL1Qx0IC6ujdZklkkASQogKwjFimkJ2dg47tm2l4PReCs9t4YdzW9isC8DH1Ija9RrTtFlTggIDtC73Fk4NpISEBBYuXIjFYmHcuHGMHj36pvXHjx9nxowZ5Obm0q5dO1555RUMBgNXrlzhhRdeICMjg/r16/P2229TpYp7n6wTQojyEhDgT9/YfkA/Lly8zMF9uym8dBzb1X1cvLaXC7vArA9A51sN3wAjQcYahIQYCQoOIiQ4iCpVfDWpW1FVVXXGC6ekpDBy5EhWrVqFp6cnI0aMYO7cuYSHhxc/JzY2lr///e+0bt2al19+mRYtWjBq1Ch+97vfERcXR79+/ViwYAH5+fm88MILpX7vjIxc7Pb7/1hGoz9paTn3vX1FID1wkD44SB8qRg9yc/M4fuw4F86dIjf9Ioo5C097Hopy8/Nsqg67okdFj6roUVEABRSFptGxdOgQdV/vr9MphIT43XG900ZIO3fuJCoqisDAQABiYmJITEzk2WefBeDy5csUFhbSunVrAAYPHsw///lPhg0bxp49e1iwYEHx42PGjLmnQBJCCHErP78qtO/QjvYd2hU/VlBQwPkLl8jMSCfnRjb5uTkUFeahWC3YbRbsdiuKCuD4Iz84ONhp9TktkFJTUzEajcXLJpOJw4cP33G90WgkJSWFrKws/Pz8MBgMNz1+L+6WwKVlNPqX+TXcnfTAQfrgIH2oqD3wp25dk9ZFAE4MpNsdCVR+My680/qStisNOWRXdtIDB+mDg/RBevCrsvShpEN2TpugHhoaSnp6evFyamoqJpPpjuvT0tIwmUwEBweTm5uLzWa76XEhhBAVm9MCKTo6ml27dpGZmUlBQQFJSUl06dKleH2tWrXw8vJi3759AMTHx9OlSxc8PDxo164d69evv+lxIYQQFZtTR0jTpk1j7NixDBw4kNjYWCIjI5k4cSJHjhwB4O233+aNN96gT58+FBQUMHbsWABmzpzJihUr6Nu3L3v37uW5555zVplCCCFchNOmfWtJziGVnfTAQfrgIH2QHvzKLc8hCSGEEPdCAkkIIYRLqJDXstPp7m2auLNew91JDxykDw7SB+nBr+63DyVtVyHPIQkhhHA/cshOCCGES5BAEkII4RIkkIQQQrgECSQhhBAuQQJJCCGES5BAEkII4RIkkIQQQrgECSQhhBAuQQJJCCGES6i0gZSQkEDfvn3p2bMny5Ytu2X98ePHGTJkCDExMUyfPh2r1apBlc5XUh82btzIgAEDiIuLY8qUKWRnZ2tQpfOV1Idfbd68mccee6wcKys/JfXgzJkzPPHEE8TFxTF+/PhKuy8cPXqUIUOGEBcXx+9+9ztu3LihQZXOl5ubS2xsLJcuXbplndO+H9VK6Nq1a2q3bt3UrKwsNS8vT+3fv7966tSpm57Tr18/9cCBA6qqqupf//pXddmyZRpU6lwl9SEnJ0ft1KmTeu3aNVVVVfWdd95RX3vtNa3KdZrS7A+qqqppaWlq79691W7dumlQpXOV1AO73a726tVL3bJli6qqqvrWW2+ps2fP1qpcpynNvjBy5Eh18+bNqqqq6htvvKHOnTtXi1Kd6uDBg2psbKzavHlz9eLFi7esd9b3Y6UcIe3cuZOoqCgCAwPx9fUlJiaGxMTE4vWXL1+msLCQ1q1bAzB48OCb1lcUJfXBYrEwa9YsQkNDAYiIiODq1atales0JfXhVzNmzODZZ5/VoELnK6kHR48exdfXt/juzZMmTWL06NFales0pdkX7HY7eXl5ABQUFODt7a1FqU61YsUKZs6ciclkumWdM78fK2UgpaamYjQai5dNJhMpKSl3XG80Gm9aX1GU1IegoCB69OgBQGFhIYsWLSperkhK6gPAp59+SrNmzWjVqlV5l1cuSurBhQsXqFatGi+++CL9+/dn5syZ+Pr6alGqU5VmX3jppZeYPn06nTt3ZufOnYwYMaK8y3S6119/nXbt2t12nTO/HytlIKm3ucC5oiilXl9RlPZz5uTkMHHiRJo0acKgQYPKo7RyVVIfTp48SVJSElOmTCnPsspVST2wWq3s3r2bMWPGkJCQQJ06dXjzzTfLs8RyUVIfCgsLmT59Op988gnbt29n1KhRvPjii+VZouac+f1YKQMpNDSU9PT04uXU1NSbhqb/uz4tLe22Q1d3V1Iffn1s1KhRNGnShNdff728SywXJfUhMTGRtLQ0hgwZwjPPPFPck4qkpB4YjUbCwsJo2bIlALGxsRw+fLjc63S2kvpw8uRJvLy8iIyMBGD48OHs3r273OvUkjO/HytlIEVHR7Nr1y4yMzMpKCggKSmp+Ng4QK1atfDy8mLfvn0AxMfH37S+oiipDzabjUmTJtGnTx+mT59eIUeJUHIfpk6dyoYNG1izZg2LFi3CZDLx+eefa1jxg1dSD9q0aUNmZiYnTpwA4LvvvqN58+Zales0JfUhLCyMa9eucebMGQA2bdpUHNKVhVO/Hx/I1Ag3tHbtWrVfv35qr1691EWLFqmqqqoTJkxQDx8+rKqqqh4/flwdMmSI2rt3b/VPf/qTajabtSzXae7Wh6SkJDUiIkKNi4sr/t/LL7+sccXOUdL+8KuLFy9WyFl2qlpyDw4ePKgOGTJE7du3r/r000+r6enpWpbrNCX1YfPmzWr//v3V2NhY9cknn1QvXLigZblO1a1bt+JZduXx/Sh3jBVCCOESKuUhOyGEEK5HAkkIIYRLkEASQgjhEiSQhBBCuAQJJCGEEC5BAkkIF/b000+TmZmpdRlClAsJJCFc2I4dO7QuQYhyI4EkhIv661//CsCTTz5ZIa+yLsT/kh/GCuHCIiIi2LVrF8HBwVqXIoTTyQhJCCGES5BAEkII4RIkkIRwYXq9HqvVqnUZQpQLCSQhXFjPnj0ZNWoUJ0+e1LoUIZxOJjUIIYRwCTJCEkII4RIkkIQQQrgECSQhhBAuQQJJCCGES5BAEkII4RIkkIQQQrgECSQhhBAuQQJJCCGES/h/ywJ6D8/eD6EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "plt.plot(expects.time / annealing_time, expects.expect[:, :6])\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('probability')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 6)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evals, evecs = ising.H_prob.eigenstates()\n",
    "e_ops = [ket2dm(ev) for ev in evecs[:6]]\n",
    "\n",
    "expects = ising.solve_sdeq(tlist, e_ops=e_ops)\n",
    "expects.expect.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "Tlist = np.geomspace(1e-2, 1e3, 50)\n",
    "\n",
    "expect_hists = {}\n",
    "for at in Tlist:\n",
    "    tlist_at = np.linspace(0, at, num_steps)\n",
    "    expects = ising.solve_sdeq(tlist_at)\n",
    "    expect_hists[at] = expects.expect[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5d6xfv7Y2QxNBVrRjO6bISKxNZVxCIapLElIQFRScZM+e3VVus3792kqnexf1l67rFO3cQVinLmXjFAohzq1BX613ctVK8lcsO+t6RVHOOxlEDRpC5ICBVW7z0ksvkJWVyaOPPsCgQUOYO/c9FEUhJaUzU6c+xMcfzycrK5MHH/wD//jH66xbt5a5c9/D4/Hg8Xh45JHp9OwpU17XN970dAL5+XL+SIgakhpSEN1334PExyfw29/exTvvvMkrr8zhnXfmYbc7eOut15kw4Vbi4xN44YWXiYiI5NNPP+b551/i7bc/5Oabb+GDD941+iWI81C0czuAjF8nRA016BpS5ICBVdZi6mrG2I0b1zFw4GCioqIBuPrqa5k588kK26iqyjPPvMDKlcs5fPgQGzasQ5XuwvVS8Y4dmOPjsSQkGB2KEPWKfOPVAU37ebOgTiAQqPBIUVERv/3tRI4fP0aPHr0YM2asnFuqh3RNo2jXTmmuE+I8SEIKIpPJRCAQoFevPqxYsYyTJ/MB+OyzhfTq1bfCNkeOHEZVVSZOvJ0+ffrxww+r0LTg195E7fIcPoxWVCjNdUKcB0lIQRQbG0dSUjIvv/wiEybcxuTJv2P8+Otxuwv43e9+D8CAAYN54IE/EB4eTvv2HRk/fgy3334zDkfYObuDi9BTdv4oRWpIQtSUotfjdqHsbPcvmsNOnDhEcnL1xg6rq3NIwVST11uVhIQIMjMLaiGi+u1Cy+HoS3/Fn51N66eeqcWojCHviXJSFuUupCxUVSEuLvzs6883KCFERbrfT/Ge3Tjk/JEQ50USkhC1pHjfXnSPB2eXrkaHIkS91CATUj1uhayRxvI664uibVtBVaWGJMR5anAJSVVNBAJ+o8OoE4GAH1U1GR2GOKVw+zYc7dpjcjiMDkWIeqnBJSSHI5yCgjx0vX53VjgXXdcoKMjF4Tj7CUJRdwIFBXgOHSRMmuuEOG8NbqSG8PAocnMzycg4ClTdpKWqaj2+1kfBarUTHh5ldCCC0tG90XXCunYzOhQh6q0Gl5AURSE2NrFa20pXTlFbCrdvRQ0Lw966jdGhCFFvVavJLicnJ9hxCFFv6bpO0bZthHXuItOVC3EBqvXpGTVqFPfffz9r18okcUL8nDc9HX9ujjTXCXGBqpWQvv32WwYMGMDzzz/P6NGjef/993G73efcb9GiRYwcOZIrrriC999//xfr9+/fz4QJE7j66qu54447yM/Pr/krEMJgRdu3Asj1R0JcoGolJLvdzvXXX8/8+fOZPn06b775JoMHD+bJJ58kOzu70n0yMjKYNWsWH3zwAZ9++inz5s1j7969Zet1Xef3v/89kyZN4rPPPqNz587MmTOndl6VEHWoaNtWLEnJWOJlugkhLkS1G7yXLVvGvffey9SpU7n88suZO3cuTZo04fe//32l269atYq0tDSio6MJCwtj+PDhLF68uGz9tm3bCAsLY8iQIQDcdddd3HTTTRf4coSoW5rPR9GunTi7Su1IiAtVrV52l1xyCTExMYwfP54XXngBu90OQEpKCvPmzat0H5fLRcIZE5QlJiayefPmsuXDhw8THx/Pww8/zPbt2+nYsSOPP/74hbwWIepcyb696F4vYV3k/JEQF6paCemFF16gX79+FR7bu3cv7du355tvvql0n8qGtVEUpey+3+9nzZo1vPfee6SmpvLSSy/x7LPP8uyzz1Y7+KpGja2uhISICz5GQyFlUaom5XDwy90oJhMtBvbDHNbwRmiQ90Q5KYtywSqLKhNSXl4eAE899RTvvvtuWZLx+/3cfffdLFmy5Kz7JiUlVeiV53K5SEwsvz4oISGBVq1akZqaCpT25JsyZUqNgq9s+omakOuQyklZlKppOWT9tB5723bkFvqhsGGVn7wnyklZlDNs+on777+ftLQ0du/ezUUXXURaWhppaWlccskldOlS9YyYAwYMYPXq1eTk5FBcXMySJUvKzhcB9OrVi5ycHHbu3AmU9uTrKu3woh7xF5zEc/iQdPcWopZUWUN64403AHj00UeZOXNmjQ6clJTE1KlTmThxIj6fjzFjxtC9e3cmTZrElClTSE1N5R//+AfTp0+nuLiY5ORknn/++fN/JULUsaIdp2aHlfNHQtSKKmeM3bdvH+3atWPbtm2Vrje6RiNNdrVHyqJUTcrhxFtv4N6wnnYvzW6QIzTIe6KclEW5YDbZVVlDeu6555gzZw733nvvL9YpinLWDg1CNHS6rlO0fSthXWS4ICFqS5UJ6fSFqt9++22dBCNEfeFNP44/NxenNNcJUWuqTEhPP/10lTtPnz69VoMRor4o2lY6XFCYdMQRotZUmZCio6PrKAwh6pfCbduwJCdjiYs3OhQhGowqE9LkyZPrKg4h6g3N56N4906iBg0598ZCiGqrMiHdeOONfPjhh/Tq1avCKAunrV+/PmiBCRGqSvbuKR0uSK4/EqJWVZmQXn75ZQA+//zzOglGiPqgcNtWMJkIS+lkdChCNChVJqTTQ/00a9aM5cuXs2rVKsxmM0OHDqVv3751EqAQoaZo2xYc7dqjnhpkWAhRO6p1AcW//vUvZs6cid1ux2QyMW3atEon3BOiofO6XHiOHCG8Zy+jQxGiwanWaN+ff/458+fPJzy89Arb2267jfHjx8v8RaLRca8rHTA4vHcfgyMRouGpVg3JZrPhdDrLlqOiorDZbEELSohQ5V6/FlvrNjI7rBBBUGUN6fT0Em3atOHuu+/mhhtuwGQysXDhQrp1kx5GonHxZWdTcmA/8deNMToUIRqkKhPSu+++W2H5rbfeKrufnZ0dnIiECFHu9aea6/pIhx4hgqFGCUmIxqxg3VqszVtgTUo2OhQhGqRqdWo4ePAg7733HkVFRei6jqZpHDp0iLlz5wY7PiFCgj8vj5J9e4m7+tdGhyJEBQHNj99XjNdbjNdXhM9XjNdXgs9fjM/vwR/w4Q948Z269Ws+/Joff8CPpgfwawEC+uk/jYAWQEND03U0XSOga2iU3jcrJm6/fDIQHZTXUq2EdP/999OtWzc2bNjAVVddxXfffWf4XEhC1CX3hnWg69JcJ2qVpmmUlORxsiCDk4VZFJWcpNjrpshbSLG/iCJ/CcUBD8WaF48WwEMAr67hQcOrgEcBn/rLUXTOh6LrmPTSnm6nb0//lS4r2FEpKXFjtUbXynP+XLUSUmFhIU8++SQzZsxgyJAhTJw4kdtuuy0oAQkRigrWrcWa3ARb02ZGhyLqiaKiXHJyj5BbcJycQhe5xbnkek9yMuChUPfhVjTcKgQqGZbtNKumY9fBoSvYULEpJiJUC1bVjE21YFMtWFUrFpMFq+n0rQ2L2VZ2azZZMZutmE0WLCZ76X2zDbPJhslkwWS2YDLZMJmqlQ6COllhtSI4Pep3q1at2LNnD927d0fTtKAEJESo8RecpHjXTmKvGmV0KCLEFBXlkpG5mxO5B3G5M3B5cnAFislWNTw/q7kouk6EBhG6iQjFShOTjQhLGBEWJxG2KCIc0Tjt0YQ5onA4oglzxGCxNK7RQKqVkFq1asWMGTO49tprmTZtGkVFRXi93mDHJkRIcG9YX9pc11ua6xorTdPIcO3mcMZWDucd5GhJDul4KDCVJx1F14kJQKJio405ghhbFDFhccREJBEX2Yzo6OaYzXL9ZlWqlZCeeOIJli1bRpcuXfjNb37DihUr+Mtf/hLs2IQICe51a7EkJGBr0dLoUEQdyT+Zzp7DP7I/Zw9HPbkcU3yUnKrxmHSdJF0lxRxFkiOOpMimJMW0ITGhA1aLw+DI67dqJSSHw0H//v357rvvaN68OTNnziQyMjLYsQlhuEBhIUU7dxBzxfBKp2ARDUN29gH2HP2Jvbn72OfNxXXqm9Gs6TTVTfSzJ9A0rAktEzrRtEk3STxBUq2EtHTpUh5++GHat2+PruscPnyYWbNm0a9fv2DHJ4Sh3Bs3QCAgzXUNTElJATv3L2Obaws7vdnkmEt/bNg0nTaKnX6OpnRM7k6r5n2wWOxBPZEvylUrIb388su89957dOjQAYBt27bx+OOPs2DBgqAGJ4TR3OvXYo6Nxd6mjdGhiAugaRonXNvZemg1208eZL/qJaAoWDSdDqqdIc5WdGjakxZNe1a7t5mofdUqeUVRypIRQNeuXdF1PWhBCREKAsXFFG3bStQll0pzXT2kaRpHjq1n3cHlbCxOJ/vUt12iDoMsiXRN6kmHtoOk+S2EVJmQ8vLyAOjWrRtvvPEG48aNQ1VVFixYQFpaWl3EJ4RhCjdvQvf7iegjTdP1haZpHEvfxLoD37Oh6DhZZlB1nfaKjWGR7enWehAJ8e2NDlOcRZUJKS0tDUVRympDL7zwQtk6RVF4+OGHgxudEAZyr1+LKSoae7t2RocizsGVuYcfdi9mQ+ERXObSLtjtFCuXRqXQq+NwIiOSjA5RVEOVCWnnzp11FYcQIUXzeCjcspnIgYNQ1GpNGybqWFFRDmt3fMGanO0cMAVQdJ22ioUhkR3p3XE4UZFNjA5R1FC1ziFpmsYbb7zBsmXL8Pv9DBw4kLvuuguzWU7+iYapcOtmdK9XmutCTCDgZ/uer/nx2I9s0d34VYV4HUbaW3FRykji46TzSX1WrYzy17/+lZ07d3LLLbegaRrz5s3jueeeY9q0acGOTwhDFPz4A6bwCBwdOhodigBy846ycvtCVhUeIt+k4NB0+lviSGs9hDYt01ClFtsgVCshLV++nI8//hiLxQLAJZdcwtVXXx3UwIQwii8nG/fGDcRc+SsUk8nocBqtgOZn557vWH50BdsoQlMUOmDl2oQ+9Og0QnrHNUDVSki6rpclIwCr1VphWYiGJH/pd6DrRA+71OhQGqWTBRms3raQlSf3kW2GME1niC2JwSlXkZzU2ejwRBBVKyF16tSJZ555hptvvhmA999/n44dz92UsWjRIl599VV8Ph+33norN910U6XbLV26lL/85S98++23NQhdiNqneb3kL/seZ89eWOLijQ6n0dA0jT0HV7Di4FI26QUEFIU2iokRsT3p02UUVqvT6BBFHahWQvrzn//M008/zbhx49B1nUGDBvH4449XuU9GRgazZs1iwYIFWK1Wxo0bx0UXXUT79hWvAcjKyuK55547/1cgRC3KXL6CgLuAmEsvNzqURqGoKIfVWxeyMm8nGebSoXvSzPEM7vArWjTrYXR4oo5VKyG99tprPPvsszU68KpVq0hLSyubS2n48OEsXryYyZMnV9hu+vTpTJ48mb/+9a81Or4QtU3XddK/+BJr02Y4OknTUDAdPLKW7/d+xYZAHj5VoQUq46K70a/LNdjtEUaHJwxS7cFV77///hod2OVykZCQULacmJjI5s2bK2zzzjvv0KVLF3r0kF9Cwngl+/ZSuG8/iTdPlKGCgsDnK2Hd9kUsc63nkCmARdPpY4phcLsraN1SuteLaiak5s2bc/vtt9O7d2+czvK23KqmMa9srLszP+S7d+9myZIl/Oc//+HEiRM1iblMXFz4ee13poQE+TV2WmMvi11vL8XkDKPtqCsxOaQHF9TOeyIz8yD/9+Ncvj95ELdJIR4YG9uFK9JuJDKi/pyna+yfjzMFqyxqNIX5tm3bMJlMREScO5ikpCTWrl1btuxyuUhMTCxbXrx4MZmZmVx//fX4fD5cLhfjx4/ngw8+qHbw2dluNO38B3mVIeXLNfay8OflkrXqB5peNYIctx/cjbcsTrvQ98TeAyv5bv//2EwhOtBJsTO06SC6dLwMk2rGUwKZJfWjnBv75+NMF1IWqqpUWZGoVkL67W9/y0MPPcSOHTvQdZ0+ffrw/PPPV7nPgAEDmD17Njk5OTgcDpYsWcJTTz1Vtn7KlClMmTIFgKNHjzJx4sQaJSMhalPe90tB00geOQK30cHUY36/h3XbPmNpxjoOmzXsus5gayJDO11DUqJcZCyqVq2E9Nhjj/Gb3/yG6667Dl3XmTdvHtOmTeOtt9466z5JSUlMnTqViRMn4vP5GDNmDN27d2fSpElMmTKF1NTUWnsRQlwI3e8n//vvcKZ2x9EkGbf8Eq6xggIXy7d+xHL3AU6eapa7PqIzA1Kvw26PMjo8UU9UKyEVFxczduzYsuUJEyYwf/78c+43evRoRo8eXeGx119//RfbNW/eXK5BEoYpWLuGwMmTREtX7xo7cmwDS3d/ybpALj61dCSFcU0G0i3lSkyqjHUpaqZa75gWLVqwfv16evfuDZR2SGjevHlQAxOiruR9+zWWpGTCunQ1OpR6we/3snHHFyw78RP7TH7Mmk4fUzTDOo6Sa4fEBalWQsrIyGDChAmkpKRgNpvZvn07CQkJZbWfRYsWBTVIIYKl5MB+SvbvJ+HGm2SaiXM4WZDB8i0fs7LwAPkmhRh0RjnaMajbdUREJJ77AEKcQ7US0kMPPRTsOIQwRO63X6PY7EQOGGR0KCEpoPnZvW8Zq46sYLNWgF9VaI+VMUkX0aPTSEwmaZYTtada76b+/fsHOw4h6pw/Px/3T2uIGjI05K47Kirxs2lvFmt3uTiRU0S4w0JkmJWIMAsRp24jnVbiouw0TwjHZqndUcmzcw7y1U+LWZG7jxyzgl3T6W+OY2jHkTRv2r1Wn0uI0+TnjWi0cpcsRvf7Q6Yzg7vYx8Y9pUlo24EcAppOTISNNk0iKSrxkZ5TxO6jXtxFPs68+k4BkmLDaJEYTsukcFokRtAiMZyYCFuNnt/nK2Hjzi9ZnbGO3YoHXVFop1gYGduD3p1HYrPJhaEiuCQhiUbJm36c3K+XEDlwMNZkY6e6PpFTxAdf72bHwVwCmk5cpJ3L+zanb0oibZpGov5sGCNN03GX+Cgo9JKRW8zhjAKOuNwcSD/JTztdZdv1bB/PLSM6EeW0Vvn8mVl7Wb5jET+WHMdtUojSdS63N2Nk/zFYrdJ5SdQdSUii0dF1HdcH76PabMRff4OhsRSV+Hn5o824i7xc2b8FfVMSaZ0cUeVYeqqqEBlmJTLMSrOEcHp3TDjjeD6OuNzsPJzHF6sP8ac3fuTWEZ3o1SGhwjECAT9bdi1m+bEf2aWWANBFcTCwSRrdOl6JyWSW0QlEnZOEJBod9/q1FO3YRsL4mzFHRhoWh6br/Pvz7WTlFfPgjb3o2CL6go8ZZreQ0jKGlJYx9E1J4PVF25n98RaG9GjKuMva4y44wupdX7D61FTgEehcbmvO4M5XExfX5sJflBAXQBKSaFQ0j4fMeR9ibd6C6KHDDI1l0cqDbNybxU1XdKyVZPRzzRLCmTaxL58s28y+w5/z1yWZHA8rPfvUHivXJfSlZ+eRmM01O9ckRLBIQhKNSs4Xi/Dn5NBi0l0optrtmVYTG/Zk8umKAwxMTebS3s1q/fiBgJ8de7/lx2M/sEUrwNdSIdqr0SojivZJQ7nmskGY5LorEWIkIYlGw5txgtwli4m4eACODsYN9JmeXci/P99O6+QIJg5PqbW5lzRN4+DhNfx0aDkbvC4KTKXdtfuaY7mo5WCaJPfnw2/28PmaDHYcXc+k0V1IjAmrlecWojZIQhKNgq7ruD58H8ViIWHMbwyLo9jj55UFWzCbVCZfl4rFfOG1tGPpW/lp3zesLzpGthlMuk5nxUHfhF70SLkSq7V8DrNJo7vSo3087yzexZ/f+onxl3dgUGoTmZBQhARJSKJRKNy4gaKtW0gYeyPmqGhDYjjdiSEjp5gHxvUkNtJ+3scqKspl5ZaPWJO/l+NmHUXXaadYuSK6M71TRuB0xp113/6dk2jfLIp/f76dt/5vJ5v3ZXPLrzoR7rCcdzxC1AZJSKLB07xeXPM+wNqsuaEXwX6x+hAb9mQx7rIOdGoVc17HyMrax7fbF/CD14VHVWiByq+dHeib8itioqt/zVBspJ0HxvXiqzWHWbBsP/uO/cgdo7rQtXXsecUlRG2QhCQavJwvv8CflUXzBx8xrCPDvmP5LFy2n7SuSVzRt+YXm+4/uJpv9n3FZgoB6KGEc2nb4bRtnXbeMamqwoi0VnRpHcucRdv469yNXNmvBdcPbVsrTYlC1JQkJNGgeY4fI/fLL4jon0ZYSidDYtB0nQ+/2UNkuLXGnRi27lrC4sPfccAUwK7rDLEmc2nX62r1mqFWyRH86dZ+zP9uL0t+OsK2Azn8dlQXEhJkqCBRtyQhiQbLn5fHsZf+hup0kvCbsefeIUjWbM9g//GT3D6yM3Zr9T5yJzJ28NGWD9iheohB59rwTgzsdj2OsOigxGizmJhwZQo92sXz1pc7ePqdtdw4PIWhqcnSPVzUGUlIokHSSoo59vdZBArdtHjoUczR53fO5kJ5fAE++n4frZIiGJCafM7ti4py+GLtmyz3ZWAGrg5rz7A+E7Fa6mY08u7t4njqjot4b8ku3vtyJ6s2Hee3o7qQHCvdw0XwSUISDY7u93P8X//Ec/QIze69D3ur1obFsmTNYXJOepg0qssvBkk9UyDgZ+XGD/kiZzOFKvRTo7mm161ER9f+RbPnEu6wcNc13RjaJ59/frSJJ95cww3D2jOsd7MqX4MQF0oSkmhQdF0n4713KNq6haSJt+FMNW7untwCD//3w2H6dEwgpeXZa2hHj2/mna3vc8ys01o3c1eHa2nT0vg5yIb0ak5ylJ23vtzB+//bzaa9Wfzu6q7SPVwEjTQOiwYl5/PPOLliGbGjRhM1ZKihsSxYto+ApnHDsHZn3ebA4TW8vO1d8hWNiXH9uP/yGSGRjE6LibAx9YYeTBiews7DufzlPz9x1OU2OizRQElCEg1G/soVZH/6CZEXDyTumusMjeXQiQJWbTnB5X1anHV4np37ljJ793+xAX/sMYmLetyAGoIdCBRFYVivZjx8U298AY0Z765j7RnzLglRW0Lv3S/EeSjcvo2Md94irHNXkm65zdChcPRT3bydDgujBrSudJstOxfz6oEviNIUpva5h6RE48bWq652TaP40y39aJ7g5J8Lt/LJsv1oun7uHYWoJklIot4r+GkNx/8xG2tyE5r8/h4Us7GnRtfvzmT3kTyuHdyGMPsvY/lpyye8fuwbEjWV+9KmEhfbuu6DPE8xETYeGt+bQd2bsGjVQV75eAvFHr/RYYkGQhKSqLc0n5eM998h/bV/YmvenOZT78cUZmz3ZJ9fY/53e2kW72RIz6a/WL9i/fu87VpFi4CZ+wY+RFSksdOnnw+LWeW2EZ246YqObN6XzdPvrCUjp8josEQDIAlJ1EvejAyOzJxB/nffEjN8BC0efMSwa43O9M26o2TmlTD20va/uKD0fz/+mw/zNtFBs3HvkMeqHAA11CmKwmV9mnP/uJ4UFPl46u21bD+YY3RYop6ThCTqnYKf1nD4qT/jy8qi6eQ/kHDDWMOb6QDy3R4WrTpAats4urWtmGz+9+PrLCzcTTfNwe8vmYbd3jCG5encKobHb+lLTISNv83bxNINx4wOSdRjxn+Khagmzeclc/5c8r/7FnvbdjS5824scaFTy5j37V58fo1xl7Wv8Pj3695hYeEeUnUHv71kGmaz1aAIgyMh2sFjE/rw2mfbeOerXRzPKmTsZb+sIQpxLpKQRMjTNY2Cn9aQ8/lneNOPEzP8V8RfOyYkakWnbTuYww/bM7h6YGuaxJVPiLd64zz+m7eFTpqdOy55tMElo9McNjNTru9eNkDriZwi7rqmW6WdOoQ4G3m3iJCl+/2c/GE1OV9+ji8jA2uTpjSdMpXw7j2MDq0Cnz/Ae1/tIjHawVUXtyp7fN3WT/kgey1tNQu/G/IIFsv5T8hXH6iqwrjLOtA03sm7X+1ixrtr+cOY7jJNuqg2SUgi5Gg+LydXriidxyg7G1vLVjT5/WTCe/VGCcFmoC9/OExGbjF//E2PsnmEtuxczNsZK2ihmbl78MPYbM5zHKXhGNKjKYnRDv7xyRaefmcd91zbrcqhk4Q4TRKSCAm6ruM9egT3xg3kff8dgbw87G3bknjTBJypPQy90LUqGblFfL76EP07J5Z1ZNix51v+ffQbkjSVewY+gN0eZXCUda9Tqxim39KXv3+0mRfnbmTC8BSG9PhlN3ghzhTUhLRo0SJeffVVfD4ft956KzfddFOF9V9//TWzZ89G13WaN2/OzJkziYpqfB/exkoPBCjesxv3xvW4N27An5UFioIjpRNxd/wOR6fOIZuIoDSJvrdkN2aTwthLOwCw98BK5hz6kjhN4d6L/1ivu3ZfqKSYMKZN6MO/Pt3Gf77cyfGsQn4zrD2qGrr/psJYQUtIGRkZzJo1iwULFmC1Whk3bhwXXXQR7duX9kByu9088cQTfPzxxyQlJfHyyy8ze/Zspk+fHqyQhME0nw/v8WN4Dh2iaPdOCjdvRisqRDGbCevSlbiRo3H26Im5nvwo+Wmni20Hchh/eQdiImwcOLyGV/ctJEJTuLf/FCIjkowO0XBhdgt/uKE7874p7+xw59VdcdikcUb8UtDeFatWrSItLY3o6GgAhg8fzuLFi5k8eTIAPp+PJ554gqSk0g9tSkoKixYtClY4og7puk7AXYDP5cJz+BAlhw7hOXwIz7GjEAgAoIaHE96zJ86evXF27YZqsxkcdc0Ulfj58Os9tEqK4NLezTl0ZC3/2PVfHMCU3ncSE93c6BBDhklVGX9FR5rGO3n/f7t55t113DumO4nRdTPpoKg/gpaQXC4XCQkJZcuJiYls3ry5bDkmJobLL78cgJKSEubMmcOECRNq9BxxceEXHGdCQsO4QLE2VKcsAh4P/pMF+ApOlt6ePIknMwuPy4UnM5OSjEw8mZloHk/ZPuaICMLbtSW+X2/C27XF2bYt9qTEkOygANUrh9cWbOZkkZc//TYNd+EuXtk5Dxvwp0vuo1nTTsEPso7U5ufjhis70bFNHM++/RPPvLuOx27tT9e29adJU74rygWrLIKWkPRKRgGu7HxAQUEBd999N506deLaa6+t0XNkZ7vRtPMfbTghIYLMzILz3r826boOp8vs1P3SMtRBO2NZ10AHNA1d00A/datp6Jpe/ngggB4IoAf86IHAGcsBdJ+v9M9feqv5fIRZVdy5BWglJWgeD1pJ8anbEnRPCYHCQgJuN7rXW2n8qtOJJS4eS0ISkZ27lt6Pj8fWoiXm2Niyf3sdcAPu7MK6KNYaq8574kD6Sb5YdYBhvZpRmLudv297FzMwpfsdWC3NQuY9daGC8floGm1n2oQ+vPzRZqa9urLedHYIpe8Ko11IWaiqUmVFImgJKSkpibVr15Ytu1wuEhMTK2zjcrm44447SEtL47HHHgtWKJVyzf2AvSuWUfno+VUkuaqG2z8zofxilV75NqE0fL+qotrtqDY7qt2OYrOh2u2YnHHYWrTEFB6BKTwcNTy87L4pPAJLbAyqvXE0v3h8Ad76v51EhFkZ2KmE2dveQwX+kHo7SUkNp2YUTEmxYUyf2IdXT3V2OJLhZuxl7TGbQrPGLOpO0BLSgAEDmD17Njk5OTgcDpYsWcJTTz1Vtj4QCHDXXXcxYsQI7r777mCFcVbObqmEOW0UF1X+i5+qencpZ1345X5nLJfVEMtuT/3n1LKiKGesK71f+pgK6qn7KKCeWqeqoKooyqlbtXQ7VBXFZEIxmVFMJjCZTi2f+rNYKvypFgsJTWLJyikK6V5tRtN1nbf+bwfHMt3cPjyM13a9B8CU1FtITu5scHT1S5jdwn03dOejpfv4as0RjmW5ufvaVJkevZELag1p6tSpTJw4EZ/Px5gxY+jevTuTJk1iypQpnDhxgu3btxMIBPjqq68A6NatGzNmzAhWSBU4u6WSMGyAVMNPUc1mSUbn8MXqQ6zZ4eLXaWY+z/oYDZjSZQJNk7sZHVq9ZFJVxl7ageYJ4by9eBd/+c9PTLm+O80TL/zcsKifFL2ykz31REM6h2Q0KYtSZyuHDXsymf3xFgZ2KmKv83v8wL2dx9Oyea+6D7KO1OV7Yv/xk8xesJkST4DfjupCn5SEc+9Uh+TzUS6Y55Ck0VaIcziW6WbOou2kNj/BTuf36DT8ZFTX2jaN5E+39KNZgpN/fLKFT1cckOnRGyFJSEJUwV3s4+8fb6ZlzG4OJ2/ArsPUHpMkGQVBTISNh8f3YmC3ZD5dcYB/LJDp0RsbSUhCnEVA03h14VYirWtJb7mbWE3lj/3/QFJiR6NDa7AsZhO3X9WZcZd1YNPebJ55dx0ZuTI9emMhCUmIs5j3zV4C3v+R3uoIzTUzfxz4oIzAUAcUReHKfi3449ge5Lk9PPWftWw9kG10WKIOSEISohLfrDvKEdd8jrTIIkWz8Ychj+F0xhsdVqPSpXUsj9/aj9hIG7Pmb2Lxj4crveBeNBySkIQ4g6bpzP9mG+v2v8bhJifppYfz+2GPY7PJsDFGSDw1PXqfjgnM/24vry/ajscXMDosESQy5K4Qp3i8AV54ayGHTV+RGacw1JzI9YPuw6TKx8RIdquZ3/+6G5+vPsTCZfs5nl3I73/djSSZibbBkRqSEEBugYfXFsxhq+MrCqxwe+JAfjPkAUlGIUJRFEYPaM2UMd3Jzi/hibd+4odtJ4wOS9QySUii0dt/1MWbS2awK/EACZrKI73upE+3a4wOS1SiR/t4nritPy0Tw5mzaDtvfrEDj1ea8BoK+fknGrWVG9bwv/T/khmjkKbHce/YaeTlybUvoSwuys5D43vx2YqDfL7qIHuP5XPXNV1pmSTn+eo7SUiiUTpZWMQnS99kk/UQigVuirmYAb2uxWJxADJETKgzqSrXDmlLp1YxzFm0jaffWcfYS9tzae9mMiZjPSYJSTQqfn+Az5fNZa13A7kOleYlKrf0uoOmTeRi1/qoc6sYnry9P29+sYP3/7ebbQdyuGVEJ6KcVqNDE+dBEpJoNFat/5bv0hdz3AGxKIxx9mPoJdejhujMtaJ6IsOsTBnTna9/OsJH3+/n8X//yM1XdqRfp0SpLdUzkpBEg7fnwFYWbf2QfU4fTovGML0911x2KxaL3ejQRC1RFYUr+7ekW9s43vhiB//6dBtrd7q4eXgKkWFSW6ovJCGJBsnr8/D9T5+zOWc9hxxeVAf0LolnzODfEhURZ3R4Ikiaxjt5bEJvvlpzhIXL97PrSB4Trkyhb6fEc+8sDCcJSTQoO/auZ8Wuxey15OA2q4RZNToXRzOix1hat+hgdHiiDphUlZFprejRLo5/f7GDfy7cSv/OiYy/oqPUlkKcJCRRr2maxv5D21m/dzm7fQdIt4Nq12lRbGGwLZVLL76GMIfT6DCFAZolhDNtQh++/PEwn604wNb9OVwzqA3DejfDbJLzhqFIEpKoVzRNY++hbWzet5pjJUdItxRTYFHBBHF+nYs8TRmaeg2tmrc1OlQRAswmldEDWtO7YwJzv9nDh9/s4bsNxxh7aXu6t4uTTg8hRhKSCFnFJYXsObCVw5l7cLnTydPycFk8pQlIBadVI9ljowfN6NKyH9069sZkMhkdtghBzeKd/PE3Pdi8L5u53+7l5Y8207VNLOMubU+zhLNPqS3qliQkYZgCdx7HMg6RmXuc3AIXJz25FAbcFOhF5Jm95FsUtFO/YBWbTpRPJ8F7KgG16k/XDr0wSwIS1aQoCj3ax9O1TSzfrT/GpysO8Oc3f2Jor6ZcPbCNXLsUAiQhiXMKBAL4/F5KPMWUeIvxej14vCX4fB683hKKfUV4PMWU+Ivx+krw+kvwBbz4NA8erQSP7sWLD68SwKtoeFSNEhOU/Lwd3woWTSfCD9F+K60DkcQ7kmmW0I6UNt2JDI8ypgBEg2I2qVzRrwUXd0tm4fL9LN1wnBWb0xnaoym/uqglsZFyOYBRGm1C+u/XczjgOQCVzPelV/bghTqjqfrsR9erXK9XuF++pFdybP1n2+lK6WN62X39jPulf5pSfqspCtoZ92tEpWzYXpOuYw/oWDWwaSo2TSUiYMXqt+BUnUTYool2xhMf1ZQmia2Ii46XZjdRJ8IdFm6+MoXL+7bg/1Yf4rsNx/huwzEGpjZhZFpLEmV6izrXaBNSia+IEiVQIVEE29meqqoQlEqyk3Lqf2X76mceRynb78xtlDOe5fTep4+j6AqqWpqNVFRUFBRUVKXsHibFhKqaMCtmTKoZ06lbi8mC1WzHbg3DbnVgt4XjsDtxhkUQHhaB0xEhCUaEtOTYMG6/qjNXD2rNlz8eZvmmdJZvPk5alyRGXtyaZvHSS7OuKHo9nhM4O9uNpp1/+AkJEWRmykCaIGVxmpRDucZaFnluD1+tOcx3G47h9Wl0bhXDVYPa0qFJOBaz/Li6kPeFqirExZ29E0mjrSEJIURlosNtjL20AyPTWrF0wzGWb07nxffX4bSbSeuazJAeTWmRKD3zgkESkhBCVCIizMrogW24akBr0vNKWLRsH99vPMY3647SOjmCwd2b0LNDAjERNqNDbTAkIQkhRBVURaFnx0SaxThwF/tYvfUEyzYf590lu3l3yW5aJUfQs308PdvH0zIpXC62vQCSkIQQoprCHRau6NeCy/s251hmIRv3ZrFpbxafrTjApysOEBNho0e7OFLbxtG+eRQRMnZejUhCEkKIGlIUheaJ4TRPDGfUgNacLPSyaV8Wm/Zms3pbBks3HgcgKTaM9s0iad8sivbNomgS70SVGtRZSUISQogLFOm0Mrh7UwZ3b4rPH+BAegF7j+Wz92g+m/Zms3LLCQAcNjOtkyNoFu+kaYKT5vHhNI13EmaXr2KQhCSEELXKYjbRsUU0HVtEA6DrOq7c4tIEdSyfwxlulm9Ox+MLlO0TE2GjWYKTpOgw4qPtxEfZiY9yEB9tx2m3GPRK6l5QE9KiRYt49dVX8fl83Hrrrdx0000V1u/YsYPp06fjdrvp27cvTz75JGaz5EghRMOhKApJsWEkxYYxMLUJAJquk5NfwtGsQo5lujmeVcixzEL2Hs2nxBuosL/DZiYu0k50hJVop42ocCuRTitRp/4inVbCHRbC7GZMav2eViNo3/4ZGRnMmjWLBQsWYLVaGTduHBdddBHt27cv2+bBBx/k6aefpmfPnjz22GPMnz+f8ePHByskIYQICaqiEB/tID7aQc/28WWP67pOkcdPVl4JWfnFZOWXkJVfQnZ+CXluD8cyCzlZ6CVwlgEBHDYzTrsZp8NSmqRsZhw2E3arGbvVhMNmxmErvW+zlP5ZLSZsFvXUrQmrRcVqNpWO3lLHgpaQVq1aRVpaGtHR0QAMHz6cxYsXM3nyZACOHTtGSUkJPXv2BOC6667j73//uyQkIUSjpSgKTrsFZ7KFVskRlW6j6TpFJX7y3R7yC73kF3opKvHjLvZRWOyjsMRHYYmfwmIfWfkllHj9lHgDeH5W8zoXk6pgNqtYTCoWc+mf027hsdv6E6zxKoKWkFwuFwkJCWXLiYmJbN68+azrExISyMjICFY4QgjRIKiKQvipGlCzhHNvf5qm6ZR4A5R4/RR7/Hh8Gh5fAK8vgNev4fUF8Jz68/s1vH4Nn1/DFyi99fs1VFXBZjHh92hBeW1BS0iVDZF35gVj51pfHVWNiVRdCQmV/wppjKQsSkk5lJOyKCdlcabgTNERtISUlJTE2rVry5ZdLheJiYkV1mdlZZUtZ2ZmVlhfHTK4au2Rsigl5VBOyqKclEW5YA6uGrQuGQMGDGD16tXk5ORQXFzMkiVLGDJkSNn6Zs2aYbPZWLduHQALFy6ssF4IIUTjErSElJSUxNSpU5k4cSK//vWvGTVqFN27d2fSpEls2bIFgBdffJGZM2cyYsQIiouLmThxYrDCEUIIEeJkPiSphgNSFqdJOZSTsignZVGuXjbZCSGEEDUhCUkIIURIkIQkhBAiJNTrgeNqY2gLI4bHCFVSFqWkHMpJWZSTsih3vmVxrv3qdacGIYQQDYc02QkhhAgJkpCEEEKEBElIQgghQoIkJCGEECFBEpIQQoiQIAlJCCFESJCEJIQQIiRIQhJCCBESJCEJIYQICZKQhBBChIR6PZZdMOzZs4c5c+YQERFBfHw8d999t9EhGe7IkSP84Q9/YMGCBUaHUufS09N54YUXcDqd9OvXj6uvvtrokAzVmN8LZ5LviVI7d+7k9ddfx+FwMGLECAYOHHhBx5OE9DO5ubk8/PDDxMfHM2nSJKPDMdzJkyeZO3cuTqfT6FAMMX/+fG677TZSU1O54447GnVCauzvhTPJ90SpoqIiHn74YcxmMy+88MIFJ6RG32Q3b948JkyYUPbXpk0b4uPjmTNnDldddZXR4dW5n5eHx+PhwQcfJCwszOjQDJGVlUVSUhIAJpPJ4GiMFRkZ2ajfC2fq379/o/6eOK13794UFhZy9913M3jw4As+XqOvIY0dO5axY8eWLXs8Hp544gkuu+yyWing+ubn5dHYJScn43K5SExMRNM0o8MRIcLj8TBz5sxG+z1x2pYtW2jbti1z587l9ttvZ+TIkRd0vEafkH7ulVdeYdu2bbjdbhYvXsyMGTOMDkkY6IYbbuC5557DZrNx/fXXGx2OCBHyPVGqpKSEadOmERsby9ChQy/8gHoDVVBQoF911VX6kSNHyh777LPP9BEjRuiXX365/t577xkYXd2T8qhIyqOclEU5KYtSRpVDg0xIGzdu1EeNGqV37dq1rEBPnDihDxs2TM/NzdULCwv10aNH63v27DE40roh5VGRlEc5KYtyUhaljCyHBtmpYf78+fz5z38mMTGx7LFVq1aRlpZGdHQ0YWFhDB8+nMWLFxsYZd2R8qhIyqOclEU5KYtSRpZDgzyHVFl7rsvlIiEhoWw5MTGRzZs312VYhpHyqEjKo5yURTkpi1JGlkODrCFVRtf1XzymKIoBkYQGKY+KpDzKSVmUk7IoVVfl0GgSUlJSEllZWWXLp7vyNlZSHhVJeZSTsignZVGqrsqh0SSkAQMGsHr1anJyciguLmbJkiUMGTLE6LAMI+VRkZRHOSmLclIWpeqqHBrkOaTKJCUlMXXqVCZOnIjP52PMmDF0797d6LAMI+VRkZRHOSmLclIWpeqqHBS9ssZBIYQQoo41miY7IYQQoU0SkhBCiJAgCUkIIURIkIQkhBAiJEhCEkIIERIkIQkhhAgJkpCEMFhKSgo5OTl88803PP3007V23OnTp7N161YApk2bxqpVq2rt2EIEg1yHJITBUlJSWL16NbGxsbV63EsvvZSXX36Z1NTUWj2uEMHSaEZqEOLnNE3jmWeeYdOmTRQWFqLrOk8//TR9+vThkUceITw8nF27dnHixAnatm3L3/72N5xOJ6mpqfzud79j5cqVuFwuJk6cyK233grAf//7Xz788EM0TSM6OprHH3+cdu3aceDAAf7yl79QVFSEy+WiU6dOvPTSS9hstrJ4FixYwFdffcVrr73GhAkT6NmzJ+vXryc9PZ0+ffrw3HPPoaoqCxYsYM6cOdjtdtLS0njnnXfYvn17hdc2a9YsXC4XDzzwAM8//zwvvvgiN910E926deOWW24hLS2NjRs34vf7eeihh5g3bx779++nW7du/O1vf0NVVdavX8+LL75IcXExiqJw7733MmzYsLr8JxKNTa3PsCREPbF+/Xr93nvv1QOBgK7ruv7aa6/pd955p67ruv7www/rY8eO1T0ej+71evVf//rX+kcffaTruq537NhRf/fdd3Vd1/UtW7bo3bp100tKSvQff/xRHz9+vF5UVKTruq4vX75cHzFihK7ruv7ss8/qCxcu1HVd171erz5q1Ch98eLFZcfLzs7WP/74Y/13v/udruu6fvPNN+tTpkzRA4GAXlBQoA8aNEhfvXq1vmfPHv3iiy/W09PTdV3X9dmzZ+sdO3as9PUNGzZM37x5c9nxvvzyS/3IkSN6x44d9a+//lrXdV3/05/+pA8bNkwvKCjQS0pK9IEDB+rr1q3T8/Ly9CuvvLLCBG1DhgzRjx07VlvFL8QvSA1JNFq9evUiKiqKuXPncuTIEX788UecTmfZ+sGDB2O1WgHo2LEj+fn5Zesuu+wyALp27YrX66WoqIilS5dy6NAhxo0bV7Zdfn4+eXl5PPjgg6xcuZLXX3+dgwcP4nK5KCoqqjK+YcOGoaoq4eHhtGrVivz8fHbu3MnAgQNJTk4G4Oabb2b27Nk1et0Wi4VLL70UgJYtW9KrVy/Cw8OB0nlu8vPz2bhxI5mZmdxzzz1l+ymKwq5du2jatGmNnk+I6pKEJBqtpUuXMmPGDG677TYuu+wy2rZty2effVa23m63l91XFKXCnDCnm9pOzwmj6zqapnHNNdfw4IMPAqVNgi6Xi6ioKKZOnUogEGDEiBFccsklpKenVzrHzJkqe36TyVRhP5PJVOPXbbFYKsxlY7FYfrFNIBCgXbt2/Pe//y17LCMjo9bPcwlxJullJxqtlStXMmzYMMaPH09qaipff/01gUDgvI83cOBAvvjiC1wuFwAffvght9xyCwArVqzgnnvuYeTIkSiKwqZNm87ruQYNGsTq1avJyMgAqJAwfs5kMuH3+8/jlUDPnj05dOgQP/30EwA7duxg+PDhZa9NiGCQGpJotMaNG8cDDzzA6NGjMZlM9O3blyVLlqBp2nkdb/DgwUyaNInbb78dRVEIDw/nlVdeQVEUpk6dyj333ENUVBQOh4N+/fpx+PDhGj9HmzZtePTRR7njjjuwWq107twZh8NR6baXX345U6dOPa+u5LGxsfz973/n+eefx+PxoOs6zz//PM2aNavxsYSoLun2LUQ9cuTIET799FPuvvtuVFVlyZIlvP7661XWlISoL6SGJEQ9kpycjMvlKqvVRURE8MwzzxgdlhC1QmpIQgghQoJ0ahBCCBESJCEJIYQICZKQhBBChARJSEIIIUKCJCQhhBAhQRKSEEKIkPD/rF2uzRRvEckAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Tlist, [sum(expect_hists[at][[0, 5]]) for at in Tlist], label=r'$|1\\rangle$')\n",
    "plt.plot(Tlist, [sum(expect_hists[at][[1, 4]]) for at in Tlist], label=r'$|2\\rangle$')\n",
    "plt.plot(Tlist, [sum(expect_hists[at][[2, 3]]) for at in Tlist], label=r'$|3\\rangle$')\n",
    "plt.plot(Tlist, [sum(expect_hists[at][:6]) for at in Tlist], label='total')\n",
    "\n",
    "plt.xscale('log')\n",
    "plt.xlabel('annealing time')\n",
    "plt.ylabel('probability')\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.00004995e-04+0.j 1.66672226e-09+0.j 2.50004164e-05+0.j\n",
      "  8.33236105e-06+0.j 2.50004164e-05+0.j 8.33236105e-06+0.j\n",
      "  4.99924992e-01+0.j 4.99924992e-01+0.j 2.50079158e-05+0.j\n",
      "  8.33486100e-06+0.j 1.66688911e-09+0.j 1.66688932e-09+0.j\n",
      "  8.33444426e-10+0.j 8.33444281e-10+0.j 8.33236105e-06+0.j\n",
      "  2.50004164e-05+0.j 2.50079158e-05+0.j 8.33486100e-06+0.j\n",
      "  8.33444426e-10+0.j 8.33444313e-10+0.j 1.66688932e-09+0.j\n",
      "  1.66688932e-09+0.j 8.33236105e-06+0.j 2.50004164e-05+0.j\n",
      "  5.00074984e-01+0.j 5.00074984e-01+0.j 8.33486100e-06+0.j\n",
      "  2.50079158e-05+0.j 8.33486100e-06+0.j 2.50079158e-05+0.j\n",
      "  1.66672196e-09+0.j 1.00004980e-04+0.j]]\n"
     ]
    }
   ],
   "source": [
    "lam = 1e-4\n",
    "H = ising.H_prob + lam * ising.H_driver\n",
    "evals_perturb, evecs_perturb = H.eigenstates()\n",
    "min_evec = evecs_perturb[np.argmin(evals_perturb)]\n",
    "print(np.transpose(min_evec))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
